Cell Cycle Modeling for Budding Yeast with Stochastic Simulation Algorithms

For biochemical systems, where some chemical species are represented by small numbers of molecules, discrete and stochastic approaches are more appropriate than continuous and deterministic approaches. The continuous deterministic approach using ordinary differential equations is adequate for understanding the average behavior of cells, while the discrete stochastic approach accurately captures noisy events in the growth-division cycle. Since the emergence of the stochastic simulation algorithm (SSA) by Gillespie, alternative algorithms have been developed whose goal is to improve the computational efficiency of the SSA. This paper explains and empirically compares the performance of some of these SSA alternatives on a realistic model. The budding yeast cell cycle provides an excellent example of the need for modeling stochastic effects in mathematical modeling of biochemical reactions. This paper presents a stochastic approximation of the cell cycle for budding yeast using Gillespie’s stochastic simulation algorithm. To compare the stochastic results with the average behavior, the simulation must be run thousands of times. Many of the proposed techniques to accelerate the SSA are not effective on the budding yeast problem, because of the scale of the problem or because underlying assumptions are not satisfied. A load balancing algorithm improved overall performance on a parallel supercomputer.